A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested two types of batteries and claimed that the batteries from Company A outperformed the batteries from Company B. A representative from Company B asked for the exact data from the study. The author of the article told the representative from Company B that in 200 tests, a battery from Company A outperformed a battery from Company B in 108 of the tests. Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name. Use Excel to test whether the true proportion of times that Company A's batteries outperformed Company B's batteries is different from 0.5. Identify the p-value, rounding to three decimal places.

p-value = 0.258

using excel the number of times company A's batteries outperformed Company B's batteries is different from the 0.5

Step-by-step explanation:

Using Excel to test whether the true proportion of times that company A's batteries outperformed company B's batteries is different from 0.5

Identify the P-value rounding to three decimal places

sample size ( n ) = 200

success ( x ) = 108

probability (p) = 0.5

Calculate the sample probability ( P ) = 108 / 200 = 0.54

Calculate the standard error ( σ )  = √(p*(1-p)/n) =  

                                                                              = √ 0.25 / 200 = 0.0354

Find the Z value

Z-value  =( P-p ) / σ

              =( 0.54 - 0.5 ) /0.035  = 0.04 / 0.0354 = 1.13

p-value = 0.258

using excel the number of times company A's batteries outperformed Company B's batteries is different from the 0.5

d

step-by-step explanation:

d

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1